In a medium bowl, whisk together the flour, cream of tartar, baking soda, cinnamon, salt, and nutmeg. Set aside.
Cream Butter and Sugars:
In a large bowl, beat the butter, granulated sugar, and brown sugar with an electric mixer on medium speed until light and fluffy, approximately 2–3 minutes.
Incorporate Wet Ingredients:
Reduce mixer speed to low and blend in the egg yolks, followed by the vanilla extract and rum extract, until fully combined.
Combine Mixtures and Chill:
Gradually add the dry ingredients to the wet mixture, mixing until just combined. Cover the bowl and refrigerate the dough for 30 minutes.
Preheat Oven:
Preheat the oven to 350°F (175°C). Line two to three baking sheets with parchment paper.
Form Cookies and Coat (Optional):
If using the sugar coating, mix granulated sugar, nutmeg, and cinnamon in a small bowl. Scoop the dough into 2-tablespoon portions, roll into balls, and coat in the sugar mixture. Place cookies 2 inches apart on prepared sheets.
Bake:
Bake for 10–12 minutes, or until edges are lightly golden and set. Allow cookies to cool for several minutes on the baking sheet before transferring to a wire rack.
Prepare the Glaze:
In a small bowl, whisk powdered sugar with 3 tablespoons of eggnog until smooth. Add an additional tablespoon if a thinner consistency is desired.
Glaze Cookies:
Once cooled, drizzle the glaze over the cookies. Allow glaze to set before serving.
Notes
To prepare these cookies gluten free, substitute the all-purpose flour with a high-quality 1:1 gluten-free baking flour that includes xanthan gum. Ensure all other ingredients, such as extracts and powdered sugar, are certified gluten free.